SophSem210: Notes for class 3

Scientific Notation

• Format d.ddddx10ⁿ.
• d's called significant figures. We use about 3.
• Converting numbers >10
  • Copy all the leading digits til reach zeros
  • Put new decimal point after first digit.
  • Write x10ⁿ where n is 1 less than number of digits to left of original decimal point.
  • Eg. 1270000 = 1.27x10⁶.
  • Eg. 4.29x10³ = 4290.
  • Eg. 6.3756x10² = 637.56.
• Converting numbers <1
  • Ignore leading zeros
  • Copy rest of digits.
  • Put new decimal point after first digit.
  • Write x10^-n where n is 1 more than number of zeros to right of original decimal point.
  • Eg. 0.0032 = 3.2x10^-3.
  • Eg. 7.23x10^-8 = 0.0000000723.
• Often use prefix letters to show common powers of 3.
  • mega is x10⁶ so eg. 12MW=12x10⁶W=1.2x10⁷W.
  • kilo is x10³ so eg. 0.57kW=0.57x10³W=570W.
  • milli is /1000 or x10^-3 so 7mW=7x10^-3W=0.007W.
  • micro is x10^-6 so 260mW=260x10^-6W=0.00026W.

Sound

• Frequency: How many repetitions or cycles in 1 second.
• Unit Hertz. 1Hz = 1 cycle/second.
• Can hear about 20Hz-20,000Hz (20kHz) when young and rather less as grow older.
• That corresponds to about 10 octaves.
• Compare piano that spans about 7+ octaves. Mine runs from 22.5Hz (low A) to about 3kHz.
• Period is duration of repetition or cycle of wave. Frequency = 1/Period.

What is a wave?

• A disturbance
• that travels through space
• without net motion of any physical object.
  • Most waves travel through a medium such as air, water, or string and involve motions of the medium. However EM waves and Gravity waves propagate through a vacuum so not an essential property!

What is a Sound Wave?

• A wave travelling through a physical medium in which the disturbance is small changes in pressure.
• The medium is most often air but most things will work. Sound travels extremely well in water, in metal, and even in bone.
• Sometimes useful to restrict to audible range (20Hz-20kHz) but inaudible sounds are still sound waves so should qualify as audible sounds if really want to restrict.

What moves in a Sound Wave?

• Air molecules move backwards and forwards making regions of locally high and low pressure.
• If wave travels left to right _ then air molecules move left-right-left _
• This is called a Longitudinal Wave.
• Contrast with a Transverse wave (eg. Water)
• In transverse, if wave moves left to right _ then particles of medium move up/down _

Motion in a Sound Wave

How to create a Sound Wave?

• Any disturbance that sets air moving creates a sound wave.
• Wave your hand (too slow to hear) or wing (hear if humming bird or mosquito).
• Make a piece of metal vibrate (eg. Bell).
• Move air rapidly as in explosion.

How long does sound last?

• Exactly as long as the disturbance that created it.
• Short disturbance -> transient sound.
• Prolonged disturbance -> steady sound.
• Periodic disturbance -> periodic sound.
• We make a special study of periodic sounds. These must last several periods to be perceived as periodic but then are of great interest because are pitched.